Question

An ice skater skates 17.5 m southwest, then 35 m east, and finally 52.5 m in a direction 49.3 degrees north of east. Find the magnitude of the displacement required to bring the skater back to her starting point.

Can you please draw a diagram for this to show how to solve please and thanks

Answer 1

Answer 2

Answer 3

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Answer 4

Decompose each vector into x (East) and y (North) components.Directions will be normalized to angles measured as the counterclockwise rotation from the x-axis (i.e. due East).

17.5 m, SW = (17.5 * cos(180 + 45), 17.5 * sin(180 + 45)) = (-12.374 , -12.374)
35 m, E = (35 * cos(0), 35 * sin(0)) =(35,0)
52.5m , 49.3 North of East = (52.5 * cos(49.3), 52.5 * sin(49.3)) = (34.235 , 39.802)

Add the x xomponents and the y components to get the skater's displacement vector (dx, dx) from the starting point.

The magnitude of the displacement vector equals the magnitude of the vector needed to return to the starting point.
| (dx, dx) | = sqrt(dx^2 + dy^2) = root (56.861^2 +27.428^2) = 63.130

Answer 5